The London side came out on top 2-1 at home to the Midlands outfit in a feisty encounter that featured two controversial pieces of refereeing with both managers frequently hopping up from their dugouts to berate the officials or query decisions.
"Paul has a certain type of personality and behaviour on the bench that pushes for that," Mourinho told reporters.
"He reminds me of myself 10 years ago when I was complaining about every decision.
"I want to coach my team and at the same time have a whistle at my lips," added the Portuguese, whose side got the better of two contentious refereeing incidents as goalscorer Branislav Ivanovic escaped a red card for an elbow and defender John Terry's clear handball was unsighted by officials.
"He is the same. He will change with experience because he complains with every decision.
"He is a young manager, and very intelligent, because he plays very well adapted to the qualities of these players. I wish him well. I like him."
While Lambert was happy to be compared with a manager who has won league titles in four countries and the Champions League twice, he took umbrage at further comments from Mourinho that suggested Villa play long-ball football.
"He is a brilliant football manager, he has done it in every country, it is a nice compliment," the Scot said.
"We are not a long-ball team, we are a football team, we don't play long ball. You look at the midfield lads, small lads, they are footballers."